DOI: 10.1111/musa.12133
TREVOR RAWBONE AND STEVEN JAN
THE BUTTERFLY SCHEMA IN THE CLASSICAL INSTRUMENTAL STYLE:A
PRODUCT OF THE TENDENCY FOR CONGRUENCE
Synthesising Associative-Statistical and Generative Theories
of Schemata through the Notion of Congruence
In the fields of music theory and music cognition, localised multiparametric
schemata receive various explications and definitions. While these cannot
be precisely pigeonholed, they do favour classification in terms of a loosely
associative-statistical or generative orientation. From an associative-statistical
standpoint, schemata form in cognition through the mental association of
statistically predominant features in time and place, such as the conglomerations
of voice-leading patterns, figured progressions and metrical structures in Leonard
B. Meyer (1973), Robert O. Gjerdingen (1988, 1996 and 2007) and Vasili Byros
(2009). For example, the 1–7 . . . 4–3 voice-leading schema appears to rise and
fall in history in a cycle of popularity and typicality resembling a bell curve,
peaking in the early 1770s, ‘due to the way brains abstract stable categories
from a continuum of historical change’ (Gjerdingen 1988, p. 99). Thus, in this
view, schemata are a form of culturally situated cognition (Gjerdingen 2007 and
Byros 2012). By contrast, in the generative paradigm, schemata emerge as stable
descriptions of the tonal grammar, generated by a system of well-formedness
and preference rules that are a product of universal cognitive capacities
(Lerdahl and Jackendoff 1983, Lerdahl 2001 and Temperley 2001), such as Fred
Lerdahl’s and Ray Jackendoff’s ‘normative structure’ (1983, p. 289). Broadly,
schemata are particular structures in associative-statistical theories, and general
or universal structures in generative theories.
In terms of underlying metaphysical foundations, the associative-statistical
programme is loosely underpinned by empiricist theories of knowledge,
following the British empiricist philosophers, including John Locke (1632–
1704), George Berkeley (1685–1753) and David Hume (1711–1776), who
were concerned with the influence of the environment or culture on behaviour.
However, the generative paradigm embraces rationalist philosophy stemming
from the ‘continental rationalism’ of Ren´ e Descartes (1596–1650), Baruch
Spinoza (1632–1677) and Gottfried Leibniz (1646–1716), which involves the
representational, combinatorial and computational structure of internal cognitive
capacities.
Notwithstanding these philosophical distinctions, both associative-statistical
and generative models incorporate primary chords, regular harmonic rhythms,
Music Analysis, 00/0 (2019) 1
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